Chapter 4: The d- and f-Block Elements (Master Student Revision Notes)

• IUPAC RULETransition Metal Definition: An element having an incompletely (partially) filled d-subshell ($d^{1-9}$) in its ground state or in any of its common oxidation states.
• EXCEPTIONGroup 12 Elements ($Zn, Cd, Hg, Cn$): Zinc ($Zn$), Cadmium ($Cd$), Mercury ($Hg$), and Copernicium ($Cn$) have completely filled $d^{10}$ subshells in BOTH ground state ($d^{10}s^2$) and common $+2$ ionic state ($d^{10}$). Thus, IUPAC classifies them as non-typical transition elements.

Unusual configurations occur due to minimal $(n-1)d$ and $ns$ energy gaps, symmetrical charge distribution, and maximum Exchange Energy ($K = \frac{n(n-1)}{2}$):

• DIP ANOMALYAnomalous Dip at Mn ($3d^5 4s^2$) & Tc ($4d^5 5s^2$): Although melting points peak at $d^5$ in the middle ($Cr, Mo, W$), $Mn$ and $Tc$ show anomalous lower melting points because stable $d^5$ binds electrons tightly, weakening interatomic metallic bonding.
• LIQUID METALMercury ($Hg$): The ONLY liquid metal at room temperature due to extremely weak metallic bonding ($5d^{10} 6s^2$).
• LOWEST ATOMISATIONZinc ($Zn, 126 \text{ kJ/mol}$): Fully filled $3d^{10} 4s^2$ has no unpaired d-electrons available for interatomic bonding.

Normally, moving down a group increases atomic size ($3d < 4d$). However, $5d$ elements have almost IDENTICAL radii to corresponding $4d$ elements!

• Cause: 14 inner $4f$ electrons filled before $5d$ series exert extremely poor shielding $\rightarrow Z_{eff}$ increases sharply by $+14 \rightarrow$ outer shells pulled inward.
• Identical Pairs to Memorize:
  • $Zr (4d) = 160 \text{ pm}$ vs $Hf (5d) = 159 \text{ pm}$
  • $Nb (4d) = 146 \text{ pm}$ vs $Ta (5d) = 146 \text{ pm}$
  • $Mo (4d) = 139 \text{ pm}$ vs $W (5d) = 139 \text{ pm}$

• NO VARIABLE STATEScandium & Zinc: $Sc$ exhibits ONLY $+3$ ($Sc^{3+}: 3d^0$). $Zn$ exhibits ONLY $+2$ ($Zn^{2+}: 3d^{10}$).
• MAXIMUM STATESManganese: Shows highest number of states ($+2$ to $+7$ in $MnO_4^-$).
• PARADOX TRENDd-Block vs p-Block Group Trend Exception:
  • In p-block, heavier elements favor LOWER states ($Pb^{2+} > Pb^{4+}$ due to inert pair effect).
  • In d-block, heavier elements favor HIGHER states! For Group 6, $Mo(VI)$ and $W(VI)$ are stable and non-oxidising, whereas $Cr(VI)$ in $Cr_2O_7^{2-}$ is a powerful oxidising agent.
• ZERO STATEMetal Carbonyls: $Ni(CO)_4$ and $Fe(CO)_5$ have metal oxidation state of ZERO ($0$) stabilized by $\pi$-backbonding.

• COPPER ANOMALYThe Copper Anomaly ($E^\circ = +0.34 \text{ V}$): Copper is the ONLY 3d metal with a positive $E^\circ(M^{2+}/M)$ value $\rightarrow$ cannot liberate $H_2$ gas from dilute mineral acids! High $\Delta_a H^\circ + IE_1+IE_2$ is NOT balanced by hydration enthalpy ($\Delta_{hyd}H^\circ$).
• REDOX PARADOX$Cr^{2+}$ Reducing vs $Mn^{3+}$ Oxidising (Both $d^4$!):
  • $Cr^{2+}$ is a strong reducing agent ($E^\circ = -0.41\text{ V}$): $d^4 \rightarrow d^3$ forms $Cr^{3+}$, which in aqueous medium has an extra stable half-filled $t_{2g}^3$ crystal field level.
  • $Mn^{3+}$ is a strong oxidising agent ($E^\circ = +1.57\text{ V}$): $d^4 \rightarrow d^5$ forms $Mn^{2+}$, attaining the extra stable half-filled $d^5$ subshell.

• NON-EXISTENCECopper Iodide Exception: $Cu^{2+}$ oxidises $I^-$ to $I_2$: $\mathbf{2Cu^{2+} + 4I^- \rightarrow Cu_2I_2(s) + I_2}$. Hence $CuI_2$ does NOT exist!
• DISPROPORTIONATION$Cu^+$ Disproportionation in Water: $\mathbf{2Cu^+(aq) \rightarrow Cu^{2+}(aq) + Cu(s)}$. Hydration enthalpy of $Cu^{2+}(aq)$ is much more negative than $Cu^+$, compensating for $IE_2$.

• COLOR EXCEPTIONLMCT Charge Transfer in $KMnO_4$: $MnO_4^-$ has $Mn(VII)$ with $3d^0$ configuration (no unpaired d-electrons). Its intense dark purple color is NOT due to d-d transition, but due to Ligand-to-Metal Charge Transfer (LMCT) ($p$-orbital of $O^{2-} \rightarrow d$-orbital of $Mn^{7+}$).
• MAGNETIC FORMULASpin-Only Formula: $\mathbf{\mu = \sqrt{n(n+2)} \text{ BM}}$ ($n$ = unpaired $e^-$). Diamagnetic: $d^0, d^{10}$ ($Sc^{3+}, Ti^{4+}, Cu^+, Zn^{2+}$).
• FERROMAGNETISMFerromagnetism: Extreme paramagnetism shown by $Fe, Co, Ni$.

• Oxidises Iodide to Iodine: $\mathbf{I^- \longrightarrow I_2}$
• $Fe^{2+} \rightarrow Fe^{3+} \quad \vert \quad C_2O_4^{2-} \rightarrow 2CO_2 \quad \vert \quad H_2S \rightarrow S \quad \vert \quad SO_3^{2-} \rightarrow SO_4^{2-}$

• CRUCIAL EXCEPTIONIodide to IODATE ($IO_3^-$): In neutral/alkaline medium, $KMnO_4$ oxidises Iodide ($I^-$) to IODATE ($IO_3^-$), NOT Iodine ($I_2$)!
  $$\mathbf{2MnO_4^- + H_2O + I^- \longrightarrow 2MnO_2 + 2OH^- + IO_3^-}$$
• $S_2O_3^{2-} \rightarrow SO_4^{2-} \quad \vert \quad Mn^{2+} \rightarrow MnO_2$

• Anomalous $+4$ and $+2$ Lanthanoid States:
  • Cerium ($Ce^{4+}$): Config $4f^0$ (noble gas config). Highly stable, but acts as a strong analytical oxidising agent ($E^\circ(Ce^{4+}/Ce^{3+}) = +1.74\text{ V}$) to revert to $+3$.
  • Europium ($Eu^{2+}$): Config $4f^7$ (half-filled). Acts as a strong reducing agent ($Eu^{2+} \rightarrow Eu^{3+}$).
  • Ytterbium ($Yb^{2+}$): Config $4f^{14}$ (fully-filled). Acts as a reductant.
  • Terbium ($Tb^{IV}$): Config $4f^7$ (half-filled). Acts as an oxidant.
• BASIC STRENGTHHydroxide Basic Strength Exception: As $Ln^{3+}$ radius decreases ($La^{3+} \rightarrow Lu^{3+}$), covalent character increases (Fajans' Rule). Thus, $La(OH)_3$ is the MOST basic, while $Lu(OH)_3$ is the LEAST basic.
• RADIOACTIVITYRadioactivity Exception: ALL Actinoids are radioactive. In Lanthanoids, ONLY Promethium ($Pm, Z=61$) is radioactive!
• GREATER CONTRACTIONActinoid Contraction Greater Exception: Actinoid contraction is greater from element to element than Lanthanoid contraction because $5f$ electrons extend further in space and exert even POORER shielding than $4f$ electrons.